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The conditions of stability are the same in the case of networks with scale-free topology where the in-and out-degree distribution is a power-law distribution: <math> P(K) \propto K^{-\gamma} </math>, and <math>\langle K^{in} \rangle=\langle K^{out} \rangle </math>, since every out-link from a node is an in-link to another.

The conditions of stability are the same in the case of networks with scale-free topology where the in-and out-degree distribution is a power-law distribution: <math> P(K) \propto K^{-\gamma} </math>, and <math>\langle K^{in} \rangle=\langle K^{out} \rangle </math>, since every out-link from a node is an in-link to another.

对于具有无标度拓扑的网络，其稳定性条件是相同的，其中进出度分布是幂律分布：<math> P(K) \propto K^{-\gamma} </math>和<math>\langle K^{in} \rangle=\langle K^{out} \rangle </math>，因为节点的每个出度链接都是到另一个节点的入度链接。

对于'''<font color="#FF8000">无标度拓扑 scale-free topology </font>'''的网络来说，稳定性的条件是一样的，其中的出入度分布是幂律分布。<math>P(K) \propto K^{-\gamma}</math>, 和 <math>\langle K^{in}\rangle=\langle K^{out} \rangle</math> ，因为从一个节点发出的每一条外链都是到另一个节点的内链。

 

Sensitivity shows the probability that the output of the Boolean function of a given node changes if its input changes. For random Boolean networks,

Sensitivity shows the probability that the output of the Boolean function of a given node changes if its input changes. For random Boolean networks,

Sensitivity shows the probability that the output of the Boolean function of a given node changes if its input changes. For random Boolean networks,

Sensitivity shows the probability that the output of the Boolean function of a given node changes if its input changes. For random Boolean networks,

<math> q_{i}=2p_{i}(1-p_{i}) </math>. In the general case, stability of the network is governed by the largest [[Eigenvalues and eigenvectors|eigenvalue]] <math> \lambda_{Q} </math> of matrix <math> Q </math>, where <math> Q_{ij}=q_{i}A_{ij} </math>, and  <math> A </math> is the [[adjacency matrix]] of the network.<ref>{{Cite journal|title = The effect of network topology on the stability of discrete state models of genetic control|journal = Proceedings of the National Academy of Sciences|date = 2009-05-19|issn = 0027-8424|pmc = 2688895|pmid = 19416903|pages = 8209–8214|volume = 106|issue = 20|doi = 10.1073/pnas.0900142106|first = Andrew|last = Pomerance|first2 = Edward|last2 = Ott|first3 = Michelle|last3 = Girvan|author3-link= Michelle Girvan |first4 = Wolfgang|last4 = Losert|arxiv = 0901.4362|bibcode = 2009PNAS..106.8209P}}</ref> The network is stable if <math>\lambda_{Q}<1</math>, critical if <math>\lambda_{Q}=1</math>, unstable if <math>\lambda_{Q}>1</math>.

<math> q_{i}=2p_{i}(1-p_{i}) </math>. In the general case, stability of the network is governed by the largest [[Eigenvalues and eigenvectors|eigenvalue]] <math> \lambda_{Q} </math> of matrix <math> Q </math>, where <math> Q_{ij}=q_{i}A_{ij} </math>, and  <math> A </math> is the [[adjacency matrix]] of the network.<ref>{{Cite journal|title = The effect of network topology on the stability of discrete state models of genetic control|journal = Proceedings of the National Academy of Sciences|date = 2009-05-19|issn = 0027-8424|pmc = 2688895|pmid = 19416903|pages = 8209–8214|volume = 106|issue = 20|doi = 10.1073/pnas.0900142106|first = Andrew|last = Pomerance|first2 = Edward|last2 = Ott|first3 = Michelle|last3 = Girvan|author3-link= Michelle Girvan |first4 = Wolfgang|last4 = Losert|arxiv = 0901.4362|bibcode = 2009PNAS..106.8209P}}</ref> The network is stable if <math>\lambda_{Q}<1</math>, critical if <math>\lambda_{Q}=1</math>, unstable if <math>\lambda_{Q}>1</math>.

<math> q_{i}=2p_{i}(1-p_{i}) </math>. In the general case, stability of the network is governed by the largest eigenvalue <math> \lambda_{Q} </math> of matrix <math> Q </math>, where <math> Q_{ij}=q_{i}A_{ij} </math>, and  <math> A </math> is the adjacency matrix of the network. The network is stable if <math>\lambda_{Q}<1</math>, critical if <math>\lambda_{Q}=1</math>, unstable if <math>\lambda_{Q}>1</math>.

<math> q_{i}=2p_{i}(1-p_{i}) </math>. In the general case, stability of the network is governed by the largest eigenvalue <math> \lambda_{Q} </math> of matrix <math> Q </math>, where <math> Q_{ij}=q_{i}A_{ij} </math>, and  <math> A </math> is the adjacency matrix of the network. The network is stable if <math>\lambda_{Q}<1</math>, critical if <math>\lambda_{Q}=1</math>, unstable if <math>\lambda_{Q}>1</math>.

<math> q_{i}=2p_{i}(1-p_{i}) </math>。 在一般情况下，网络的稳定性由矩阵<math> Q </math>的最大特征值<math> \lambda_{Q} </math>决定，其中<math> Q_{ij}=q_{i}A_{ij} </math>和<math> A </math>是网络的邻接矩阵。 如果<math>\lambda_{Q}<1</math>是稳定的网络，如果<math>\lambda_{Q}=1</math>是关键的网络，如果<math>\lambda_{Q}>1</math>，则不稳定。

<math> q_{i}=2p_{i}(1-p_{i}) </math>。在一般情况下，网络的稳定性由最大的特征值<math>\lambda_{Q}</math>来控制。的矩阵 <math>Q</math>，其中<math> Q_{ij}=q_{i}A_{ij}</math>，<math>A</math> 是网络的邻接矩阵。如果 <math>\lambda_{Q}<1</math>，网络是稳定的；如果 <math>\lambda_{Q}=1</math>，网络是临界的；如果 <math>\lambda_{Q}>1</math>，网络是不稳定的。

 

== Variations of the model ==

== Variations of the model ==